Problem: ${6 \div \dfrac{3}{5} =}$
Explanation: $6 \div \dfrac{3}{5}} ={\dfrac61} \div \dfrac{3}{5}} $ $~~~~~~~{\gray{\text{Rewrite 6 as }\dfrac61.}} $ $\phantom{6 \div \dfrac{2}{3}}} ={\dfrac61} \times \dfrac{5}{3}}$ $ ~~~~~~{\gray{\text{Multiply by reciprocal of }\dfrac35.}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{6\timesD5}{1\timesD3}} $ $~~~~~~~{\gray{\text{Multiply. }}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{30}{3}} $ $~~~~~~~{\gray{\text{Simplify. }}} $ $\phantom{8 \div \dfrac{2}{3}}} =10 $ ${6 \div \dfrac{3}{5} =10}$